A combinatorial representation of links by quasitoric braids
type: Item
instance of: scholarly article
title: A combinatorial representation of links by quasitoric braids
zbMATH Open document ID: 0991.57007
published in: European Journal of Combinatorics
publication date: 2002-08-28T00:00:00Z
review text: According to Alexander's theorem, every link admits a representation by a closed braid. Markov proved that two braids \(\alpha\) and \(\beta\) represent the same link if and only if \(\alpha\) can be transformed to \(\beta\) by using a sequence of local transformations called Markov moves. In the present paper, the author introduces the notion of quasitoric braids and shows that all link isotopy classes can be encoded by quasitoric braids. It is worth mentioning that quasitoric braids represent a very small class of braids that forms a subgroup of the braid group. This subgroup contains the pure braids.
reviewed by: Nafaa Chbili
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 20F36
zbMATH DE Number: 1740610
zbMATH Keywords: pure braids
author: V. O. Manturov
MaRDI profile type: Publication
full work available at URL: eujc.2001.0546
OpenAlex ID: W1970850313
cites work: Q4844975
cites work: Theory of braids
cites work: FREE KNOTS AND GROUPS
cites work: Threading knot diagrams
cites work: Q5687983
cites work: Representation of links by braids: A new algorithm
DOI: 10.1006/EUJC.2001.0546
description: scientific article; zbMATH DE number 1740610